Question

Suppose an ant walks counterclockwise on the unit circle from the point to the endpoint of the radius that forms an angle of radians with the positive horizontal axis. How far has the ant walked?

Answer 1

`(4\pi)/(3)`

Explanation:

The original questions is suppose an ant walks counterclockwise on a unit circle from the point (1,0) to the endpoint of the radius that forms an angle of 240 degrees with the positive horizontal axis.

To find the distance ant walked we find the arc length of the sector with central angle 240 degree and radius =1 (unit circle)

arc length of a sector =
`(centralangle)/(360) \cdot 2\pi r`

arc length of a sector =
`(240)/(360) \cdot 2\pi(1)`

arc length of a sector =
`(2)/(3) \cdot 2\pi`

`(4\pi)/(3)`